On the subject of "why hasn't anyone on Earth seen the terraforming", I think it's mostly because it's not like they can see lifeforce suddenly shooting through the roof. I mean, our technology modern day can't detect the essence of life. Signs of it, maybe, but not the pure essence that the fairies from hell were exuding. I do think that it's odd they didn't see any of the danmaku happening, though. Stage 5 looks to be on the "real" surface of the Moon that we see ourselves in the Outside World. We can't see Stage 6 because that's in the "dream/fantasy" surface of the Moon, but as I said before, to quote a CinemaSins joke: "Nobody who watches the sky for a living sees this shit." Remember, Stage 5 and 6 are on the near side of the moon, the side we can always see, so if someone didn't see some sort of weird lightshows happening up there, I'd be amazed. The same can be applied to ULiL, where it seems no one is aware of the danmaku fights that were occurring above whichever city the protagonists were dumped into near the end of their stories.
Still, between both games, the Outside World has had visible danmaku fights in it, and whether or not people have noticed... well I can't say for certain. So far there seems to be no story details on that end, but I'm wondering if it's possible there's now rumors of strange happenings.